Explaining cancer dynamics with game theory

February 28, 2009

 Building a tumour takes teamwork!

Isolated groups of few cancer cells generally do not give rise to new tumours. Micrometastases, i.e. very small clusters of tumour cells, can frequently be found in the lymph nodes and bone marrow of cancer patients. These micrometastases tend to lie dormant after removal of the primary tumour – often for the remainder of the patient’s life. Moreover, it is well known that much cancer surgery leads to a veritable spraying of cancer cells in the operation wound, but it is very rare that these cells form any metastases where they land.

It is only a few years since the mainstream view of cancer researchers turned towards viewing the tumour as a complex society of cells, including tumour cells of heterogeneous natures, supporting stromal cells, and ingrowing blood vessels. These cells all have to work together in order for the tumour to grow and progress. It is a hotly debated issue whether the stromal and vascular cells are deceitfully co-opted by tumour cells which secrete growth factors similar to those occurring e.g. in wound healing, or whether the non-cancer cells surrounding the cancer cells are in themselves supporting and accelerating the tumour growth and progression.

It is in this complex tissue interplay that the tumour cells live and evolve. Cancer cells are genetically dissimilar from the people that are their hosts and progenitors, because they accumulate genetic changes of various kinds – mutations, deletions, amplifications, translocations – that enable them to proliferate independently and so on. One common first step in carcinogenesis is a genetic destabilisation, which leads to a much increased rate of genetic change. Hence, tumour cells constantly develop new genotypes and phenotypes and grow into a heterogeneous society of cells.

Now, in almost every situation where cooperation exists, dynamics come into play that are described by game theory. If everyone cooperates, it is typically advantageous for a single organism or cell to defect and reap the rewards of everyone else’s cooperativity while not contributing. This incentive to defect can lead to the collapse of the cooperative system, or to the emergence of a counter-strategy which rewards cooperators and punishes defectors. Against these strategies, in turn, there are other counter-strategies, and so the play of Nature continues. We can observe it in populations of bacteria, honey bees, wolves, and humans. And in cancer, or so we expect.

But what does it mean for a cancer cell to defect, and cease to cooperate? For about ten years, scattered groups of scientists have been building models where tumour cells of two different kinds derive certain benefits and drawbacks from being next to other cells of the same or of the other kind. (See this paper for a review.) Models like these are great fun, and they highlight the importance of evolutionary dynamics within the tumour. But thus far, the fitness modifiers have been very arbitrarily chosen, and can hardly be said to represent the physical realities of the tumour except on a very abstract level.

There are two conceptual problems that make it very difficult to conceive of what defection in a tumour cell would look like. The first is that the cancer cell bathes in the same soup of growth factors as its immediate neighbours, and many of the stimulatory signals that are emitted by the cancer cell end up targeting the cell itself – so-called autocrine stimulation. This means that if the cancer cell were to stop stimulating its neighbours, it would also stop stimulating itself, and that would hardly ever result in any fitness increase. The second problem is that the cost of signalling is very low, and most of the cooperative behaviour takes the form of signalling through secreted molecules. That means that even if another cell has something to lose if the first cell stops its signalling, the first cell has almost nothing to gain. (Anti-proliferative signalling by tumour cells is very uncommon. I do not know of any proven example.)

In a recent paper, D. Basanta and co-workers suggest a biochemical basis for an act of defection, coupled to game-theoretical interactions. Their model brings in the Warburg effect, which is common to tumours of nearly all kinds. It consists in a shift from aerobic to anaerobic metabolism – great for when the blood supply is strained, as it usually becomes when tumours grow beyond a few millimetres in size. According to their reasoning, cells that shift their metabolism in this way adversely affect their neighbours, because they release toxic metabolites. They proceed to construct a set of conditions under which invasive tumour cells start to migrate out from the tumour after sufficiently many cells have turned anaerobic. In fact, they provide a completely new theoretical framework that may explain in evolutionary terms why the Warburg effect is so ubiquitous.

As good theory should, this model yields predictions that are testable in principle. Unfortunately, it is not really possible to eliminate locally the toxic by-products of anaerobic metabolism, or to prevent the Warburg effect from appearing at all. While we wait for experimental science to catch up, these theoretical models continue to help us form a tentative understanding of the principles behind the tissue interactions in tumours.

Update: The Carnival of Evolution has just been published in its ninth edition at Moneduloides, and this post has been included!

Nature endorses science blogging

February 27, 2009

The latest issue of Nature carries an editorial encouraging scientists to blog about their research. It discusses how to relate to public discussion of unpublished results, and ends by saying:

”[…] there are societal debates that have much to gain from the uncensored voices of researchers. A good blogging website consumes much of the spare time of the one or several fully committed scientists that write and moderate it. But it can make a difference to the quality and integrity of public discussion.”

This is obviously something to keep in the desk drawer for any scientist who keeps a blog and who may run into a discussion with colleagues or department heads about whether it is valuable to spend time on writing about science in this format.

However, good science blogs have been around for years. The reason why this endorsement comes now is probably the joint impact of the blogosphere and preprint servers. In mathematics and physics, it is very common to upload manuscripts to arxiv.org before they are submitted to peer-reviewed journals. Nature has started a similar preprint server for the biological and medical sciences. These preprints may be discussed by the authors on their own blogs, or by other readers in the scientific community. In the past, the same kinds of discussions would occur only in the physically limited space of conferences or through personal contacts. Now, discussions about new science can be carried out before the eyes of the world, with links directly to the findings so that everyone can make their own interpretation. The monopoly of the scientific journals is evaporating. Nature appears to have realised now that this is a development they cannot hinder, and therefore they reluctantly accept it. Seen from this perspective, the editorial represents a walk-over victory for open science!

I can see through your forehead!

February 24, 2009

Well, what to make of this? The Zooillogix blog alerts me to a new report on the barreleye, a bizarre deep-sea fish. It has recessed its eyes quite deep underneath the skin of the forehead, which is completely translucent! Over the mouth are two small dots that look like eyes, but are in fact nostrils of a sort.

Check out this video:

Deep sea news has more coverage.

How cells decide to live or die: an ambitious effort at the MIT to map the wiring

February 24, 2009

At the first glance, it may not be obvious why a cell should have anything to benefit from deciding to kill itself. But in a multicellular organism, cells often need to be replaced. An average homo sapiens turns over about 3 kg of her body weight each day, through cell death and proliferation. If a cell were to lose its proper judgement and stop responding to death signals, it would remain and possibly proliferate at the expense of the other cells and the organism. We have a word for it: cancer.

Therefore, scientists have spent lots of effort trying to understand how cell death is regulated. Most of the time, these efforts have centered on specific genes and proteins. Researchers have been able to remove or inhibit one protein, say, and found that cell death decreases. They have meticulously mapped together interacting proteins in models with arrows, that resemble at best a mechanical contraption where each protein is a cogwheel and the rotation of one is directly proportional to another, etc.

The MIT Cell Decision Process Center is populated by scientists that feel that the nonlinear dynamics in the cell can only be understood with more mathematically sophisticated methods. Yet at the same time, they believe that little comes of speaking in general terms about complexity (as I am prone to do) without backing it up with rock-solid biological data. They have embarked on a quest to extract enormous amounts of very detailed information from the cells’ interior, that can serve as a basis for modelling. In the words of Peter Sorger, the centre’s director: “In its emphasis on formal numerical models, systems biology breaks with the tradition in genetics and molecular biology of anecdotal and pictorial models. However, the experimental emphasis in is also critical because it is only through experimentation that models can be tested for their accuracy. “

This is a completely reductionist approach to the cell, implying that the system can best be understood in terms of its components. Such approaches tend to be very cumbersome, because they need to generate huge quantities of data to determine the dynamics of many components at once. It is research by the Verdun doctrine: throw more people and equipment at the problem, and it will eventually surrender. It is the opposite of trying to find an incisive point where a key hypothesis can be tested. It is often productive research, but in the end it’s not really a lot of fun to do.

Do I want to work at this centre? Well, they seem to be the largest and best place in the world where the anatomy of the cell’s brain is being explored. But their actual work consists of data-grinding. They do fun things too, mainly in methods development – for example, they have developed a set of weighing scales capable of telling the weight of cell substructures and nanoparticles. But I continue to hope that the organising principles of the cell’s brain can be understood with a holistic approach, aimed at finding the rules that govern it.

Cells in context: when a single neuron makes the decision

February 23, 2009

The brain, our most magnificent organ, is among other things a generator of decisions. It routinely receives input, matches it against an internal representation about the exterior world, and adjusts our behavior in appropriate ways. (More often appropriate than not, that is.)

In our staggeringly complex human brains, it is impossible to pinpoint any decision to a single cell. Most researchers subscribe to a model where decisions in the brain are determined by the architecture and dynamics of the neural network, i.e. the synaptic connections, transmissions, and responses.

But what happens in a nerve system with less than our approx. 1014 connections? Brain sizes come in a huge continuum, ranging from 4-5 kg in the elephant, over approximately 1.3 kg in the human, down to invertebrates with only a few nerve cells in their entire bodies. Yet all these creatures share the ability to make decisions.

With diminishing complexity in the nervous system, the actual decision should become easier and easier to pinpoint, and eventually it might converge on a single cell. This is in fact what has been found in the Aplysia, a sea slug with a fairly simple and very well-characterised nervous system, and a common model organism in neuroscience. A neuron called B51 has been shown to make the decision to carry out feeding behaviour. Successful feeding is rewarded by dopaminergic signaling from the esophagus back to neuron B51. This is known in psychology as operant conditioning, meaning roughly that the organism learns from the consequences of its behavior.

A recent paper by Fred Lorenzetti and co-workers in the journal Neuron begins to shed light on how decision-making is carried out by neuron B51. Lorenzetti and his colleagues found that reward of the feeding behavior led to changes in the membrane structure of the neuron, reducing the threshold for firing and therefore making it more probable that feeding behavior will be initiated. They were also able to block the activities of a few intracellular proteins, and found two protein kinases that were crucial for operant conditioning to take place.

We can attribute meaning to these biochemical changes. In its context, a reduced firing threshold of neuron B51 probably means that there is a greater abundance of food in the environment. This piece of knowledge is a part of the internal representation of the outside world. And this particular cell possesses enough complexity to both carry this part of the internal representation and function as a decision generator on its own!

Of course, since the cell is part of the neural network this doesn’t mean that a network-centered view is any less correct or useful. The information processing of neuron B51 can only be made meaningful in the context of its neuronal connections. And it is not necessary to know, from a network-perspective, which specific changes in the cell that are underpinning the cell’s altered electrical activity. And finally, as a caveat, I should add that much is still unknown about the regulation of neuron B51. This model may well have to be questioned in the light of future evidence.

But this story illustrates three important things:

  • That a single cell can be capable of making decisions

  • That the internal workings underlying decision-making in the cell are attracting attention, although more from neurobiologists than from cell biologists.

  • That the decisions of single cells in multicellular organisms may require other cells to decode the decision and translate it into behavior, which means that the decision is only meaningful in that highly specific context.

Can a single cell be intelligent?

February 19, 2009

The quest to find intelligent behavior in animals has been a long one, and it has unraveled some rather spectacular examples. Witness, just to mention a few, crows creating their own tools, sea slugs that learn through conditioning, and magpies who can recognise their own reflection in a mirror.

How complex does an animal have to be in order to show signs of intelligence? Not very, according to Toshiyuki Nagakaki and his co-workers, who claim to have seen intelligent behavior in the slime mold. This fascinating and beautiful life form consists of single cells that often live separately but that are able to join up and form an organism consisting of a single cell with very many nuclei. Thus, the cell nuclei can exist in two radically different levels of social complexity.

In their paper, Nagakaki et al have used the slime mold physarum polycephalum. This mold forms a network with pulsating tubes between food sources. Essentially, what they have been able to show is that the physarum is able to optimise its network structure to form the shortest route between several food sources. Furthermore, it is able to do so in a labyrinth that the scientists had constructed.

Encouraged by this result, Soichiro Tsuda and his colleagues at the University of Southampton have tried a radical approach: they have built a robot controlled by a slime mold brain. In this case, they are using the physarum’s predilection for darkness to let it steer the robot, and they have apparently succeeded in building a system that consistently walks the robot away from light. (Their article gives a brilliant example of the kind of lucid reasoning in which mathematicians and physicists excel.)

These examples challenge the definition of intelligence, but in my opinion they fall short. In neither case does the system show any adaptive behavior. The mold is only able to solve a labyrinth problem by testing all possibilities, i.e. by growing into all parts of the maze and then retracting from those where no food was found. And in the robot case, the mold functions by giving a specific response to a specific stimulus, which any transistor setup could accomplish as easily.

Tsuda and his colleagues note that biological systems display an enviable combination of adaptivity and robustness. Artificial systems have, until now, been unable to replicate this successful trade-off. Tsuda’s proposed solution is to put biological systems in control of the computers, but there exists a different and more appealing way forward. We can learn to understand biological information processing! When we are able to formulate a functional principle-driven model of the cell’s brain, we will be able to replicate it with silicon components.

The secret of Life

February 16, 2009

Few people have ever been convinced they had found the Secret of Life. And those who were convinced of it have often not remained so for very long. Robert Brown (1773-1858), for example, thought he had found it when he observed pollen grains in water under a microscope and saw them moving independently of each other. He interpreted it as evidence of an indivisible unit of life, capable of forming new flowers. It later emerged that any inorganic matter can show the same sort of random motion, now termed Brownian motion.

Francis Crick (1916-2004) announced in 1953, together with James Watson (1928-), that he had found the secret. He was referring to the structure of DNA, the landmark discovery with which his name will always be connected. Many people erroneously credit him for something else also: the discovery of the genetic code. In fact, it was the brilliant physicist George Gamow (1904-1968) who was first to realise that the four-base variations of the DNA molecule constitute a code.

But are we there yet?

Any living organism, even the simplest bacterium, performs innumerable complex activities that cannot possibly be deduced from the genetic sequence alone. We have found the main repository of information, but we are still fumbling in the dark when it comes to the principles for deciding what information to read, and when, and why.

Even the simplest units of life exhibit extremely robust and well-regulated behavior. A protozoan looking for food decides to go in one direction, and not the other. A cell of a slime mold decides to sacrifice itself for the greater good of the community. These actions are governed by a vast network of interconnecting signaling mediators, most of them proteins.

Scientists working on these networks have, for the most part, a mental model of the cell resembling a machine composed of cog-wheels. Endless hours are spent trying to find out which wheel grabs on to which. Huge tabulations are made with arrows indicating either stimulation or inhibition of one protein on another.

These models are drawn in the face of our massive understanding that biological systems tend to be non-linear and dynamic. If I poke the system gently and upset one of the signaling molecules, it is for the most part impossible to tell what changes will follow in the complex system.

At the same time, this very complexity gives rise to new phenomena on a system level. Robustness and stability towards certain stimuli are coupled with remarkable adaptability to others. Higher-order conformity to laws of behavior appear.

The biological system takes information and creates meaning. We do not know how.

This is the next frontier, and possibly the final one, in our quest for the secret of life.